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Conformal holonomy
equals ambient holonomy
Andreas Čap, A. Rod Gover, C. Robin Graham and Matthias Hammerl |
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Vol. 285 (2016), No. 2, 303–318
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Abstract |
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We study the relation between two notions of holonomy on a conformal manifold. The first is the conformal holonomy, defined to be the holonomy of the normal tractor connection. The second is the holonomy of the Fefferman–Graham ambient metric of the conformal manifold. It is shown that the infinitesimal conformal holonomy and the infinitesimal ambient holonomy always agree up to the order that the ambient metric is defined. |
Keywords
holonomy, ambient metric, tractor, conformal geometry
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Mathematical Subject Classification 2010
Primary: 53A30
Secondary: 53C29
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Milestones
Received: 3 April 2015
Revised: 9 March 2016
Accepted: 8 June 2016
Published: 21 November 2016
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Authors |
| Andreas Čap | |
| Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 1090 Wien Austria |
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| A. Rod Gover | |
| Department of Mathematics The University of Auckland Private Bag 92019 Auckland 1142 New Zealand |
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| C. Robin Graham | |
| Department of Mathematics University of Washington Box 354350 Seattle, WA 98195-4350 United States |
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| Matthias Hammerl | |
| Department of Mathematics and
Informatics University of Greifswald Walther-Rathenau-Str. 47 D-17489 Greifswald Germany |
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